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| '''Luminosity distance''' ''D<sub>L</sub>'' is defined in terms of the relationship between the [[absolute magnitude]] ''M'' and [[apparent magnitude]] ''m'' of an astronomical object.
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| :<math> M = m - 5 (\log_{10}{D_L} - 1)\!\,</math>
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| which gives:
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| :<math> D_L = 10^{\frac{(m - M)}{5}+1}</math>
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| where ''D<sub>L</sub>'' is measured in [[parsec]]s. For nearby objects (say, in the [[Milky Way]]) the luminosity distance gives a good approximation to the natural notion of distance in [[Euclidean space]].
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| The relation is less clear for distant objects like [[quasar]]s far beyond the [[Milky Way]] since the apparent magnitude is affected by [[spacetime]] [[curvature]], [[redshift]], and [[time dilation]]. Calculating the relation between the apparent and actual luminosity of an object requires taking all of these factors into account. The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance.
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| Another way to express the luminosity distance is through the flux-luminosity relationship. Since,
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| :<math> F = \frac{L}{4\pi D_L^2}</math>
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| where ''F'' is flux (W·cm<sup>−2</sup>), and ''L'' is luminosity (W), or where ''F'' is flux (erg·s<sup>−1</sup>·cm<sup>−2</sup>), and ''L'' is luminosity (erg·s<sup>−1</sup>). From this the luminosity distance can be expressed as:
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| :<math> D_L = \sqrt{\frac{L}{4\pi F}}</math>
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| The luminosity distance is related to the "comoving transverse distance" <math>D_M</math> by the Etherington's reciprocity relation:
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| :<math> D_L = (1 + z) D_M</math>
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| where ''z'' is the [[redshift]]. <math>D_M</math> is a factor that allows you to calculate the [[comoving distance]] between two objects with the same redshift but at different positions of the sky; if the two objects are separated by an angle <math>\delta \theta</math>, the comoving distance between them would be <math>D_M \delta \theta</math>. In a spatially flat universe, the comoving transverse distance <math>D_M</math> is exactly equal to the radial comoving distance <math>D_C</math>, i.e. the comoving distance from ourselves to the object.<ref>{{cite book| author = Andrea Gabrielli| coauthors = F. Sylos Labini, Michael Joyce, Luciano Pietronero| title = Statistical Physics for Cosmic Structures| url = http://books.google.com/?id=nYHRdjxKOEMC&pg=PA377| date = 2004-12-22| publisher = Springer| isbn = 978-3-540-40745-4| page = 377 }}</ref><ref>http://www.mpifr-bonn.mpg.de/staff/hvoss/DiplWeb/DiplWebap1.html {{dead link|date=January 2013}}</ref>
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| ==See also==
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| * [[Distance measures (cosmology)]]
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| * [[distance modulus]]
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| == Notes ==
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| {{reflist}}
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| ==External links==
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| * [http://www.astro.ucla.edu/~wright/CosmoCalc.html Ned Wright's Javascript Cosmology Calculator]
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| * [http://icosmos.co.uk/ iCosmos: Cosmology Calculator (With Graph Generation )]
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| [[Category:Observational astronomy]]
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| [[Category:Physical quantities]]
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| {{relativity-stub}}
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Let me initial begin by introducing myself. My title is Boyd Butts even though it is not the title on my beginning certification. Puerto Rico is where he's always been residing but she needs to move because of her family members. My working day job is a meter reader. To gather cash is a factor that I'm totally addicted to.
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